A372615 Number of regions among all distinct circles that can be constructed from the 3 vertices and the equally spaced 3*n points placed on the sides of an equilateral triangle, using only a compass.

7, 121, 624, 2368, 7912, 17115, 38461, 63184, 115614, 170149, 285715, 371982, 588043

Offset

0,1

Comments

A circle is constructed for every pair of the 3 + 3*n points, the first point defines the circle's center while the second the radius distance.

The vertices of the initial equilateral triangle are indicated by small circles in the illustrations here.

Links

Table of n, a(n) for n=0..12.

Scott R. Shannon, Image for n = 0.

Scott R. Shannon, Image for n = 1.

Scott R. Shannon, Image for n = 2.

Scott R. Shannon, Image for n = 3.

Scott R. Shannon, Image for n = 4.

Formula

a(n) = A372616(n) - A372614(n) + 1 by Euler's formula.

Crossrefs

Cf. A372614 (vertices), A372616 (edges), A372617 (k-gons), A372682 (number of circles), A371374, A353782, A360352.

Sequence in context: A196583 A197041 A283625 * A095752 A113267 A274267

Adjacent sequences: A372612 A372613 A372614 * A372616 A372617 A372618

Keyword

nonn,more

Author

Scott R. Shannon, May 07 2024

Status

approved